The country's weather service issued a warning that as much as 3 inches of rain could fall as Jose approached the island with 40 mph winds and higher gusts.
The system was moving northward at 16 mph with gusts that didn't reach the hurricane threshold of 74 mph, the U.S. National Hurricane Center in Miami said.
The storm was expected to weaken by Sunday night and diminish Monday over cooler Atlantic Ocean waters, forecasters said.
Winds from the center of Jose extended outward for 50 miles, the report said.
Earlier this week, the island felt only minor coastal effects from Hurricane Irene, which affected the U.S. Eastern Seaboard and reached New York Sunday as it dropped to tropical storm status.